What is the maximum B-field in the iron core?

[Clari]

A student wishes to light a lamp rated 12V, yet he has only a 2V rms a.c supply with variable frequency. So he attempts to step up the voltage by means of a transformer. Given Ns:Np = 6:1, resistance in the primary circuit is 70 ohm, inductance of primary coil is 0.3H, frequency f is 50Hz

a.) If Ns = 600, Vs = 10V (rms), cross-sectional area of the secondary coil is 2cmx2cm, what is the maximum B-field in the iron core?

i find this question really difficult, because my teacher uses differentiation to solve it... i wonder if there are simple ways to solve it. Thanks!

 

[lightgrav]

$$\frac{\Delta (B \cdot A)}{\Delta t} = E \cdot circumference$$ .

in 1/200 sec (that is, .005 s), B changes from zero to its maximum.
You might expect that the greatest rate of change in B is 200/s times B_max ;
but in fact, the greatest rate of change in B is (2 pi f) times B_max .
(recall velocity of an oscillator?)
This is why you really need to take derivitives.